Starting from the detailed description of the single-collision decoherence mechanism proposed by Adami, Hauray and Negulescu (2016 R. Adami, M. Hauray, C. Negulescu. 2016. Decoherence for a heavy particle interacting with a light particle: new analysis and numerics. Comm. Math. Sci. 14 (5):1373–1415.[Crossref], [Web of Science ®] , [Google Scholar]), we derive a Wigner equation endowed with a decoherence term of a fairly general form. This equation is shown to contain well known decoherence models, such as the Wigner–Fokker–Planck equation, as particular cases. The effect of the decoherence mechanism on the dynamics of the macroscopic moments (density, current, energy) is illustrated by deriving the corresponding set of balance laws. The issue of large-time asymptotics of our model is addressed in the particular, although physically relevant, case of Gaussian solutions. It is shown that the addition of a Caldeira–Legget friction term provides the asymptotic behavior that one expects on the basis of physical considerations.

从对Adami，Hauray和Negulescu（2016年）提出的单冲突去相干机制的详细描述开始 R.阿达米， M. Hauray， C. Negulescu。2016。重粒子与轻粒子相互作用的退相干：新的分析和数值。通讯 数学。科学 14（5）： 1373 – 1415。[Crossref]，[Web of Science®]， [Google Scholar]），我们得到一个Wigner方程，该方程具有相当一般形式的退相干项。在特定情况下，该方程式包含众所周知的退相干模型，例如Wigner-Fokker-Planck方程式。通过导出对应的一组平衡律，可以说明去相干机制对宏观矩（密度，电流，能量）动力学的影响。我们的模型的长时间渐近性问题在高斯解的特殊情况下（尽管在物理上相关）解决了。结果表明，增加Caldeira–Legget摩擦项可提供人们根据物理考虑而期望的渐近行为。